Title: DOEbased Automatic Process Control with Consideration of Model Uncertainties
1DOE-based Automatic Process Control with
Consideration of Model Uncertainties
Jan Shi and Jing Zhong The University of
Michigan C. F. Jeff Wu Georgia Institute of
Technology
2Outline
- Introduction
- DOE-based Automatic Process Control with
Consideration of Model Uncertainty - Process model
- Control objective function
- Controller design strategies
- Simulation and case study
- Summary
3Problem Statement
- Process variation is mainly caused by the change
of unavoidable noise factors. - Process variation reduction is critical for
process quality improvement. - Offline Robust Parameter Design (RPD) used at the
design stage - To set an optimal constant level for controllable
factors that can ensure noise factors have a
minimal influence on process responses - Based on the noise distribution but not requiring
online observations of noise factors - Online Automatic Process Control (APC) during
production - With the increasing usage of in-process sensing
of noise factors, it will provide an opportunity
to online adjust control factors to compensate
the change of noise factors, which is expected
to achieve a better performance than offline RPD.
4Motivation of Using APC
y(x,e)
xx1
?b
?a
e
noise distribution
5The Objective and Focus
The research focuses on the development of
automatic process control (APC) methodologies
based on DOE regression models and real-time
measurement or estimation of noise factors for
complex mfg processes
6Literature Review
- For complex discrete manufacturing processes, the
relationship between the responses (outputs) and
process variables (inputs) are obtained by DOE
using a response surface model, rather than using
dynamic differential/difference equations - offline robust parameter design (RPD) (Taguchi,
1986) - Improve robust parameter design based on the
exact level of the observed uncontrollable noise
factors (Pledger,1996) - Existing APC literature are mainly for automatic
control of dynamic systems that are described by
dynamic differential/difference equations. - Certainty Equivalence Control (CEC) (Stengel,
1986) The controller design and state estimator
design are conducted separately (The uncertainty
of system states is not considered in the
controller design) - Cautious Control (CC) (Astrom and Wittenmark,
1995) The controller is designed by considering
the system state estimation uncertainty, which is
extremely difficult for a complex nonlinear
dynamic system. - Jin and Ding (2005) proposed Doe-Based APC
concepts - considering on-line control with estimation of
some noise factors. - No interaction terms between noise and control
factors in their model.
7Objective
- Develop a general methodology for controller
design based on a regression model with
interaction terms. - Investigate a new control law considering model
parameter estimation uncertainties - Compare the performances of CC, CEC, and RPD, as
well as performance with sensing uncertainties.
8Methodology Development Procedures ? APC Using
Regression Response Models
Obtain significant factors estimated process
model
S1 Conduct DOE and process modeling
Based on key process variable
S2 Determine APC control strategy (considering
model errors
Use certainty equivalence control or cautious
control
Based on observation uncertainty
Based on process operation constraints on
controller
S3 Online adjust controllable factors
Obtain reduced process variation
S4 Control performance evaluation
91. Process Variable Characterization
Process Variables
Noise Factors
Controllable Factors
Off-line setting Factors
Unobservable Noise Factors
On-line adjustable Factors
Observable Noise Factors
Y f (X, U, e, n)
102. Control System Framework
Observable Noise Factors (e)
Unobservable Noise Factors (n)
Noise Factors
Target
Feedforward Controller
Manufacturing Process
Response (y)
Controllable Factors (x)
Predicted Response
In-Process Sensing of e
Observer for Noise Factors (e)
113 Controller Design3.1 Problem Assumptions
- The manufacturing process is static with smoothly
changing variables over time Parameter Stability
- e, n and e are independent, with E(e)0,
Cov(e)Se, E(n)0, Cov(n)Sn, E(e)0, Cov(e)Se.
e are i.i.d.
- Estimated process parameters denoted by
, - is estimated from
experimental data.
- Observations of measurable noise factors, denoted
by , are unbiased, i.e.,
and .
123 Controller Design 3.2 Objective Function
Objective Function (Quadratic Loss)
Optimization Problem
133 Controller Design 3.3 Control Strategy
Procedure for Solving Optimization Problem
Step 2 obtain X by solving optimization problem
of JAPC
Process Control Strategy Two Step Procedure
Step 1 Off-line Controllable Factors Setting
Step 2 On-line Automatic Control Law
144. Case Study An Injection Molding Process
Process Description
Response Variable (y) Percentage
Shrinkage of Molded Parts
Process Variables
15DOE Modeling
Designed Experiment Result (Engel, 1992)
Reduced DOE Model after Coefficient Significance
Tests
Parameter Estimation Error
16Robust Parameter Design
Response Model
Variance Model
RPD Settings
u1 and x3 are adjusted according to target values
as in right table
17DOE-Based APC
Objective Loss Function
Optimal Settings
where
18Simulation Results
Comparison of RPD, CE control and Cautious Control
Assuming
Optimal Off-line Setting
Cautious control law performs much better than RPD
Control Strategy Evaluation
19Simulation Results - 2
Certainty Equivalence assume observation perfect
CE controller performs much better than RD when
the measurement is perfect, but its advantage
decreases when the measurement is not perfect,
and will cause a larger quality loss than RPD
controller under high measurement uncertainty.
20Control strategy with partial sensing failure 1
- Sensor noise level change no modeling error
150 observations, sensor noise level increased
from point 51 to 100, then restored. t1.6
CE Control suffers greatly from noise level change
Mean of RPD has deviated from target
21Control strategy with partial sensing failure 2
- Sensor noise level change
APC considering modeling error
255 observations, sensor noise level increased
from point 101 to 200, then restored
Overall J/J_ce16.8. APC performance is steady
over different noise levels.
22Control strategy with partial sensing failure 3
- Assume no modeling error, - 250 observations,
sensor failed from point 51 to 150, then repaired
Control Strategy
Switch to RPD setting after the detection of
sensor failure - Actual system will have step
response
23Industrial Collaboration with OG Technologies
DOE-Based APC Test bed in Hot Deformation
Processes
24Summary
- DOE-Based APC performs better than RPD when
measurable noise factors are present with not too
large measurement uncertainty. - RPD should be employed in case of too large
measurement uncertainty or there are no
observable noise factors. - Cautious control considering measurable noise
factors and model estimation uncertainty performs
better than RPD and CE strategy. - Model updating and adaptive control with
supervision are promising or the future study.
25Impacts
- Expanding the DOE from off-line design and
analysis to on-line APC applications, and
investigates the associated issues in the DOE
test design and analysis - Developing a new theory and strategy to achieve
APC by using DOE-based models including on-line
DOE model updating, cautious control, and
supervision.